On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers

This paper presents a new experimental approach to the Weber problem in the presence of convex barriers by using the Varignon frame. The Varignon frame is a mechanical system of strings, weights and a board with holes that has been used to identify an optimal location for the classical Weber problem. We show through analytical results that the same analog can also be used for some of the Weber problems in the presence of barriers. Some examples from the literature are revisited through experiments. Findings are compared to those found in the literature. Practical use of the analog is discussed as it provides rapid solutions, allows for flexibility, and enables one to visualize the problem.     

Concentration-Dependent Seeding as a Strategy for Fabrication of Densely Packed Surface-Mounted Metal–Organic Frameworks (SURMOF) Layers

The layer-by-layer (LbL) method is a well-established method for the growth of surface-attached metal–organic frameworks (SURMOFs). Various experimental parameters, such as surface functionalization or temperature, have been identified as essential in the past. In this study, inspired by these recent insights regarding the LbL SURMOF growth mechanism, the impact of reactant solutions concentration on LbL growth of the Cu₂(F₄bdc)₂(dabco) SURMOF (F₄bdc²⁻=tetrafluorobenzene-1,4-dicarboxylate and dabco=1,4-diazabicyclo-[2.2.2]octane) in situ by using quartz-crystal microbalance and ex situ with a combination of spectroscopic, diffraction and microscopy techniques was investigated. It was found that number, size, and morphology of MOF crystallites are strongly influenced by the reagent concentration. By adjusting the interplay of nucleation and growth, we were able to produce densely packed, yet thin films, which are highly desired for a variety of SURMOF applications.     

一个新的空间掩盖效应拟合公式

传统的空间掩盖效应是采用韦伯（Weber）定律来描述的，然而该定律仅考虑了明视觉区，对较弱或较强的光强均不合适。为了更好地描述空间掩盖效应，本文利用信号处理方法，给出了一种新的拟合公式。实验用不同模型拟合Konig与Brodhun的实验数据，证实了提出的模型均方根误差仅为0．0102，小于传统的Weber定律、Weber定律的优选表达式、Guilford模型，以及Chen模型。结果表明，提出的拟合公式在更宽的光强范围内都能与数据很好地拟合，可更广泛地用于工程实践。     

微波场协同提取红龙果食用红色素的研究

研究了应用微波从红龙果（Hylocereus Costaricensis or Weber Britt）中提取食用红色素的新工艺，并确定了最佳工艺条件：提取剂为50％的乙醇溶液，原料用量（g）与提取剂用量（mL）比为1：90。微波功率为700W，提取时间为20s，提取次数为4次。最佳工艺条件下的色素提取率为98．94％，产品pH值为6。与溶剂浸提法相比，微波法提取红龙果食用红色素的每次提取时间由2h减少到20s，提取率从90．96％增加到98．94％。     

An Order-theoretic Framework for the Greedy Algorithm with Applications to the Core and Weber Set of Cooperative Games

An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in R ⁿ . This model unifies various generalizations of combinatorial models in which the greedy algorithm and the Monge algorithm are successful and generalizations of the notions of core and Weber set in cooperative game theory.As a further application, we show that an earlier model of ours as well as the algorithmic model of Queyranne, Spieksma and Tardella for the Monge algorithm can be treated within the framework of usual matroid theory (on unordered ground-sets), which permits also the efficient algorithmic solution of the intersection problem within this model.     

A new local search for continuous location problems

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulation space search. The local search is applied to the multi-source Weber problem where encouraging results are obtained. This local search is also embedded within Variable Neighbourhood Search producing excellent results.     

On the Fermat–Weber center of a convex object

We show that for any convex object Q in the plane, the average distance from the Fermat–Weber center of Q to the points in Q is at least Δ(Q)/7, where Δ(Q) is the diameter of Q, and that there exists a convex object P for which this distance is Δ(P)/6. We use this result to obtain a linear-time approximation scheme for finding an approximate Fermat–Weber center of a convex polygon Q.     

Carl Neumann’s Contributions to Electrodynamics

I examine the publications of Carl Neumann (1832–1925) on electrodynamics, which constitute a major part of his work and which illuminate his approach to mathematical physics. I show how Neumann contributed to physics at an important stage in its development and how his work led to a polemic with Hermann Helmholtz (1821–1894). Neumann advanced and extended the ideas of the Königsberg school of mathematical physics. His investigations were aimed at founding a mathematically exact physical theory of electrodynamics, following the approach of Carl G.J. Jacobi (1804–1851) on the foundation of a physical theory as outlined in Jacobis lectures on analytical mechanics. Neumanns work also shows how he clung to principles that impeded him in appreciating and developing new ideas such as those on field theory that were proposed by Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879).Karl-Heinz Schlote works as a historian of mathematics in the Arbeitsgruppe für Geschichte der Naturwissenschaften und Mathematik at the Sächsische Akademie der Wissenschaften in Leipzig, Germany.     

Uniform asymptotic formulae for the spheroidal angular function

The problem of wave scattering by a spheroid is treated. Special interest is paid to the solution of the differential wave equation related to the angular spheroidal functions. A solution is obtained using uniform asymptotic formulae along with semiclassical methods. The developed method shows that it is possible to interpolate uniformly the spheroidal angular function with Weber's parabolic cylindric functions and Legendre's functions.     

Planar weber location problems with line barriers

The Weber problem for a given finite set of existing facilities in the plane is to find the location of a new facility such that the weithted sum of distances to the existing facilities is minimized.

A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers like rivers, highways, borders or mountain ranges are frequently encountered in practice.

Structural results as well as algorithms for this non-convex optimization problem depending on the distance function and on the number and location of passages through the barrier are presented.